Research Interests for David P. Kraines

Research Interests:Algebraic Topology and Game Theory

Dr. Kraines contributed to the theory of homology and
cohomology operations, particularly to Massey products and
loop operations. Among the applications of his work has
been his construction of the counterexample to the
transfer conjecture of Quillen. He has also studied the
variational bicomplex of Vinogradov and introduced the
cohomology of quantum electrodynamics.
Dr. Kraines has applied game theoretical techniques to
study the evolution of cooperation. With Dr. Vivian
Kraines,
he introduced a stochastic learning approach, dubbed
the Pavlov strategy, for the iterated Prisoner's Dilemma.
They show that, in a noisy environment, agents using
the Pavlov strategy may achieve a higher level of
cooperation
than those using Tit for Tat type strategies. Using
computer simulations, dynamic systems and Markov
chains, they
extend their analysis to the evolution of the rate of
learning in a society of Pavlov type agents. Recently,
they have
explored the natural selection of stochastic strategies
in the simultaneous and the alternating Prisoner's
Dilemma and identified several evolutionarily stable
strategies.